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Byju's Answer
Standard XII
Mathematics
Greatest Integer Function
Let ln=2n+-2n...
Question
Let
l
n
=
2
n
+
(
−
2
)
n
2
n
and
L
n
=
2
n
+
(
−
2
)
n
3
n
then as
n
→
∞
A
Both the sequences have limits.
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B
lim
n
→
∞
l
n
exists but
lim
n
→
∞
L
n
does not exist.
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C
lim
n
→
∞
l
n
does not exist but
lim
n
→
∞
L
n
exists.
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D
Both the sequences do not have limits.
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Solution
The correct option is
C
lim
n
→
∞
l
n
does not exist but
lim
n
→
∞
L
n
exists.
l
n
=
2
n
+
(
−
2
)
n
2
n
=
1
+
(
−
1
)
n
⇒
lim
n
→
∞
l
n
=
{
0
if
n
is odd
2
if
n
is even
So,
lim
n
→
∞
l
n
does not exist.
L
n
=
(
2
3
)
n
(
1
+
(
−
1
)
n
)
⇒
lim
n
→
∞
L
n
=
0
Suggest Corrections
0
Similar questions
Q.
Evaluate:
lim
n
→
∞
3
n
−
2
n
3
n
+
2
n
Q.
The value of
lim
n
→
∞
3
n
+
2
n
3
n
−
2
n
is
Q.
lim
n
→
∞
(
2
n
+
1
+
3
n
+
1
2
n
+
3
n
)
is equal to
Q.
If
lim
n
→
∞
(
1
1
+
√
n
+
1
2
+
√
2
n
+
1
3
+
√
3
n
+
⋯
+
1
2
n
)
=
log
e
k
, then
k
=
Q.
lim
n
→
∞
3
n
+
1
+
2
n
+
2
3
n
−
1
+
2
n
−
2
is equal to
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